U.S. patent number 9,922,289 [Application Number 14/870,663] was granted by the patent office on 2018-03-20 for quantum nondemolition microwave photon counter based on the cross-kerr nonlinearity of a josephson junction embedded in a superconducting circuit.
This patent grant is currently assigned to INTERNATIONAL BUSINESS MACHINES CORPORATION. The grantee listed for this patent is International Business Machines Corporation. Invention is credited to Baleegh Abdo.
United States Patent |
9,922,289 |
Abdo |
March 20, 2018 |
Quantum nondemolition microwave photon counter based on the
cross-Kerr nonlinearity of a Josephson junction embedded in a
superconducting circuit
Abstract
A technique relates to a microwave device. A pump resonator, at
a first pump resonator end, is connected to both a dispersive
nonlinear element and a first stub. The pump resonator, at a second
pump resonator end, is capacitively coupled to a pump port, where
the first stub is terminated in an open circuit. A quantum signal
resonator, at a first quantum signal resonator end, is connected to
both the dispersive nonlinear element and a second stub. The
quantum signal resonator, at a second signal resonator end, is
capacitively coupled to a signal port, where the second stub is
connected to ground.
Inventors: |
Abdo; Baleegh (Carmel, NY) |
Applicant: |
Name |
City |
State |
Country |
Type |
International Business Machines Corporation |
Armonk |
NY |
US |
|
|
Assignee: |
INTERNATIONAL BUSINESS MACHINES
CORPORATION (Armonk, NY)
|
Family
ID: |
58407393 |
Appl.
No.: |
14/870,663 |
Filed: |
September 30, 2015 |
Prior Publication Data
|
|
|
|
Document
Identifier |
Publication Date |
|
US 20170091647 A1 |
Mar 30, 2017 |
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01P
7/082 (20130101); H01P 1/20381 (20130101); G01V
8/005 (20130101); G01R 23/02 (20130101); G06N
10/00 (20190101) |
Current International
Class: |
H03K
3/38 (20060101); G01R 23/02 (20060101); H01P
7/08 (20060101); G01V 8/00 (20060101); H01P
1/203 (20060101); G06N 99/00 (20100101) |
Field of
Search: |
;327/528,527,524 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
A Poudel, et al.,"Quantum efficiency of a microwave photon detector
based on a current-biased Josephson junction", American Physical
society, Vo. 4, No. 17, Nov. 6, 2012, p. 1-4. cited by applicant
.
B. Fan, et al.,"Nonabsorbing high-efficiency counter for itinerant
microwave photons," Physical Review B, vol. 90, No. 3, Jul. 25,
2014, pp. 1-5. cited by applicant .
B. Peropadre, et al.,"Approaching perfect microwave photodetection
in circuit QED," Physical Review A, vol. 84, No. 6, Dec. 14, 2011,
pp. 1-8. cited by applicant .
Baleegh Abdo,"Quantum Nondemolition Microwave Photon Counter Based
on the Cross-Kerr Nonlinearity of a Josephson Junction Embedded in
a Superconducting Circuit", U.S. Appl. No. 14/952,133, filed Nov.
25, 2015. cited by applicant .
C. K.Andersen, et al.,"Quantized resonator field coupled to a
current-biased Josephson junction in circuit QED", American
Physical Society, vol. 89, No. A, Mar. 27, 2014, p. 1-9. cited by
applicant .
G.Romero, et al.,"Microwave Photon Detector in Circuit QED,"
Physical Review Letters, vol. 102, No. 17, May 1, 2009, pp. 1-4.
cited by applicant .
J. Bourassa, et al.,"Josephson junction-embedded transmission-line
resonators: from Kerr medium to in-line transmon" arXiv, vol. 2,
Jul. 17, 2012, p. 1-15. cited by applicant .
K. Koshino, et al., "Dressed-state engineering for continuous
detection of itinerant microwave photons," Quantum Physics, Sep.
2015, pp. 1-7. cited by applicant .
L. C.G. Govia, et al.,"High-fidelity qubit measurement with a
microwave-photon counter", The American Physical Society, vol. 90,
Dec. 2, 2014, p. 1-12. cited by applicant .
List of IBM Patents or Patent Applications Treated as Related;
YOR920150780US1, Date Filed: Sep. 30, 2015, p. 1-2. cited by
applicant .
O. Suchoi, et al.,"Intermode dephasing in a superconducting
stripline resonator", American Physcial Society, No. 81, May 24,
2010, p. 1-8. cited by applicant .
S.R. Sathyamoorthy, et al.,"Quantum Nondemolition Detection of a
Propagating Microwave Photon," Physical Review Letters, vol. 112,
No. 9, Mar. 7, 2014, pp. 1-5. cited by applicant .
Y-F. Chen, et al.,"Microwave Photon Counter Based on Josephson
Junctions," Physical Review Letters, vol. 107, No. 21, Nov. 18,
2011, pp. 1-5. cited by applicant.
|
Primary Examiner: Skibinski; Thomas
Attorney, Agent or Firm: Cantor Colburn LLP Alexanian;
Vazken
Claims
What is claimed is:
1. A microwave device comprising: a dispersive nonlinear element; a
pump resonator, at a first pump resonator end, connected to both
the dispersive nonlinear element and a first stub, the pump
resonator, at a second pump resonator end, being capacitively
coupled to a pump port, wherein the first stub is terminated in an
open circuit; and a quantum signal resonator, at a first quantum
signal resonator end, connected to both the dispersive nonlinear
element and a second stub, the quantum signal resonator, at a
second signal resonator end, being capacitively coupled to a signal
port, wherein the second stub is connected to ground.
2. The microwave device of claim 1, wherein the dispersive
nonlinear element is at least one Josephson junction.
3. The microwave device of claim 1, wherein the dispersive
nonlinear element is an array of Josephson junctions.
4. The microwave device of claim 1, wherein the pump resonator
comprises a pump resonance mode, the pump resonance mode having a
pump resonance frequency and a pump wavelength; wherein a length of
the pump resonator corresponds to a quarter wavelength of the pump
wavelength; wherein the quantum signal resonator comprises a signal
resonance mode, the signal resonance mode having a signal resonance
frequency and a signal wavelength; wherein a length of the quantum
signal resonator corresponds to a quarter wavelength of the signal
wavelength; and wherein the pump resonance mode and the signal
resonance mode are coupled to the dispersive nonlinear element.
5. The microwave device of claim 4, wherein by having the pump port
and the signal port spatially separated and by having the pump
resonance mode and the signal resonance mode isolated from each
other via the first and second stubs, no direct power leakage
occurs between the pump and signal ports; wherein the pump
resonator and the quantum signal resonator are configured such that
pump resonance mode acquires a frequency shift according to a
number of photons in an input quantum signal at the signal
resonance frequency.
6. The microwave device of claim 5, wherein the pump resonator and
the quantum signal resonator are configured such that a cross-Kerr
nonlinear effect is generated in the dispersive nonlinear element
in response to an input pump signal, thereby creating a nonlinear
interaction between the pump resonance mode and the signal
resonance mode.
7. The microwave device of claim 6, wherein the cross-Kerr
nonlinear effect causes a reflected pump signal at the pump
resonance frequency to be dependent on the number of the photons in
the input quantum signal at the signal resonance frequency.
8. The microwave device of claim 7, wherein the pump resonator is
configured such that the reflected pump signal at the pump
resonance frequency carries information about a presence or absence
of the photons in the input quantum signal.
9. The microwave device of claim 6, wherein the cross-Kerr
nonlinear effect causes a reflected quantum signal at the signal
resonance frequency to be dependent on a number of photons in the
input pump signal at the pump resonance frequency.
10. The microwave device of claim 5, wherein the pump resonator is
configured such that a size of the frequency shift in the pump
resonance frequency is determinative of the number of the photons
in the input quantum signal.
11. The microwave device of claim 5, wherein the pump resonator,
the quantum signal resonator, the first and second stubs, and the
dispersive nonlinear element are configured to neither destroy nor
absorb the photons in the input quantum signal while the frequency
shift of the pump resonance mode counts the number of the photons
in the input quantum signal.
Description
BACKGROUND
The present invention relates to measurement techniques of quantum
systems operating in the microwave frequency domain, such as
superconducting quantum circuits, and more specifically, to
detection and/or counting of single microwave photons in a
nondemolition manner.
A photon is an elementary particle, the quantum of light and all
other forms of electromagnetic radiation. A photon carries energy
proportional to the radiation frequency and has zero rest mass.
One reason why the detection of single microwave photons is an
outstanding challenge is because the energy of a single microwave
photon is very small. The energy of a photon in the microwave
domain, for example in the range 1-10 gigahertz, is at least
10.sup.4 times smaller than the energy of a visible light
photon.
Circuit quantum electrodynamics (cQED) is one of the leading
architectures for realizing a quantum computer based on
superconducting microwave circuits. It employs artificial atoms
made of nonlinear superconducting devices called qubits which are
dispersively coupled to microwave resonators, i.e., the frequencies
of the qubits and resonators are detuned. As one example, each
superconducting qubit may comprise one or more Josephson junctions
shunted by capacitors in parallel with the junctions. The qubits
are capacitively coupled to two-dimensional (2D) planar waveguide
resonators or three-dimensional (3D) microwave cavities. The
electromagnetic energy associated with the qubit is stored in the
Josephson junctions and in the capacitive and inductive elements
forming the qubit. To date, a major focus has been on improving
lifetimes of the qubits in order to allow calculations (i.e.,
manipulation and readout) to take place before the information is
lost due to decoherence of the qubits.
Dispersively coupling a superconducting qubit to a microwave
resonator in a cQED architecture loads the resonator and makes its
resonance frequency dependent on the quantum state of the qubit
(i.e., the resonance frequency of the resonator is different
depending on whether the qubit is in the ground or excited states).
This property enables the performance of quantum nondemolition
measurement of the qubit state, by sending a microwave signal on
the order of a few photons to the cQED near the resonator
frequency, and measuring the amplitude and/or phase of the output
microwave field that carries information about the qubit state.
Thus, one potential application of a working and reliable single
photon detector in the microwave domain is to enable measuring this
weak output signal (i.e., detecting the qubit state) inside the
dilution fridge, without requiring the use of high-gain, low-noise,
and high-isolation output chains that are typically used nowadays
in order to perform such measurements.
SUMMARY
According to one embodiment, a microwave device is provided. The
microwave device includes a dispersive nonlinear element, and a
pump resonator, at a first pump resonator end, connected to both
the dispersive nonlinear element and a first stub. The pump
resonator, at a second pump resonator end, is capacitively coupled
to a pump port, where the first stub is terminated in an open
circuit. Also, the microwave device includes a quantum signal
resonator, at a first quantum signal resonator end, connected to
both the dispersive nonlinear element and a second stub. The
quantum signal resonator, at a second signal resonator end, is
capacitively coupled to a signal port, wherein the second stub is
connected to ground.
According to one embodiment, a method for nondemolition counting of
photons is provided. The method includes coupling a pump resonance
mode of a pump resonator and a signal resonance mode of a quantum
signal resonator to a dispersive nonlinear element, responsive to a
pump signal at a pump resonance frequency and a quantum signal at a
signal resonance frequency. The pump resonance mode of the pump
resonator has the pump resonance frequency, where the signal
resonance mode of the quantum signal resonator has the signal
resonance frequency. Also, the method includes creating a nonlinear
interaction between the pump signal and the quantum signal, by
driving the pump resonance mode with the pump signal at the pump
resonance frequency, and detecting a presence or absence of photons
in the quantum signal according to the pump resonance frequency
which affects an output pump signal being measured.
According to one embodiment, a method of operating a microwave
device is device. The method includes receiving, by the microwave
device, a pump signal at a pump resonance frequency, where the pump
resonance frequency corresponds to a pump resonance mode of a pump
resonator. The method includes receiving, by the microwave device,
a quantum signal at a signal resonance frequency, where the signal
resonance frequency corresponds to a signal resonance mode of a
signal resonator, and outputting, by the microwave device, the pump
signal with a phase shift, in response to a number of photons in
the quantum signal.
Additional features and advantages are realized through the
techniques of the present invention. Other embodiments and aspects
of the invention are described in detail herein and are considered
a part of the claimed invention. For a better understanding of the
invention with the advantages and the features, refer to the
description and to the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic of a microwave device according to an
embodiment.
FIG. 2 is a schematic of an equivalent circuit of the microwave
device as seen by the pump port according to an embodiment.
FIG. 3 is a schematic of an equivalent circuit of the microwave
device as seen by the signal port according to an embodiment.
FIG. 4 is a schematic of an example implementation of the microwave
device using a coplanar waveguide geometry according to an
embodiment.
FIG. 5 is a schematic of an example implementation of the microwave
device using a microstrip geometry according to an embodiment.
FIG. 6 is a flow chart of a method for nondemolition counting
and/or detection of photons using the microwave device according to
an embodiment.
FIG. 7 is a flow chart of a method for the microwave device
according to an embodiment.
DETAILED DESCRIPTION
In the optical frequency domain, reliable single photon detectors
such as photomultipliers, microwave kinetic inductance detectors,
and superconducting nanowire single-photon detector are widely used
in various experiments and applications. However, one disadvantage
of these devices is that they destroy (i.e., absorb) the photons
that they detect.
In contrast, in the microwave domain, i.e., the gigahertz (GHz)
range, reliable and practical single photon detectors are still
under research and development. A working microwave photon detector
based on Josepshon junctions (dubbed the Josephson photomultiplier)
has been experimentally researched. However, similar to single
photon detectors in the optical domain this device absorbs the
photons it detects. Additionally, this microwave device under
development does not count the number of photons present in an
incoming signal, it can only distinguish between the cases of zero
photons or at least one photon in the signal.
Embodiments provide a practical scheme for a microwave device and
measurement method for counting single microwave photons.
Embodiments are configured to 1) detect and count the number of
single photons within a certain bandwidth in the microwave domain,
(i.e., in the gigahertz (GHz) range, e.g., the 1-20 GHz range), and
2) perform the detection and counting of photons in a nondemolition
manner, i.e., without destroying (or absorbing) the photons being
detected or counted.
Now turning to the figures, FIG. 1 is a schematic of a microwave
device 100 according to an embodiment. The microwave device 100
includes a quarter-wavelength resonator 102 for the pump drive and
a quarter-wavelength resonator 104 for the quantum signals. One end
of the pump resonator 102 is connected to a coupling capacitor
106A, and the coupling capacitor 106A connects to a pump feedline
108. The pump feedline 108 is connected to pump port 111 and/or the
pump port 111 is on the pump feedline 108. The pump feedline 108
receives a microwave pump signal 130 (i.e., a strong microwave
tone), from a microwave generator 135 (denoted as pump). The other
end of the pump resonator 102 connects to both a dispersive
nonlinear element, e.g., Josephson junction (JJ) 110 and connects
to a half-wavelength stub at the pump frequency 120A. The
connection of the pump resonator 102, Josephson junction (JJ) 110,
and stub 120A may be designated as node A. Opposite the node A, the
stub 120A is terminated in an open circuit (O. C.). Opposite the
coupling capacitor 106A, the pump feedline 108 is connected to a
microwave measurement/analysis device 150. The microwave
measurement/analysis device 150 is configured to measure the pump
signal 130 in reflection after pump signal 130 has interacted with
microwave device 100. The microwave measurement/analysis device 150
may include and/or be connected to a computer for determining the
phase shift (in the frequency) in the pump signal as discussed
further herein. The microwave measurement/analysis device 150 may
include and/or be connected to one or more processors, memories
(e.g., computer readable storage medium) display screens, input
devices (e.g., mouse, keyboard, touch screen, etc.). The pump 135
and microwave measurement/analysis device 150 are operatively
connected to the microwave device 100 via a circulator 180A but are
not part of the microwave device 100.
In the microwave device 100, one end of the quarter wavelength
signal resonator 104 is connected to a coupling capacitor 106B, and
the coupling capacitor 106B connects to a signal feedline 109. The
signal feedline 109 is connected to a signal port 113 and/or the
signal port 113 is on the signal feedline 109. The signal feedline
109 is configured to receive a microwave quantum signal 140, i.e.,
microwave signal being measured/tested, from a quantum device 145.
The quantum device 145 may be a qubit, a cavity coupled to a qubit,
etc. The other end of the signal resonator 104 connects to the
Josephson junction (JJ) 110 and connects to a half-wavelength stub
at the pump frequency 120B. The connection of the pump resonator
102, Josephson junction (JJ) 110, and stub 120B may be designated
as node B. Opposite the node B, the stub 120B is terminated in a
short-circuit. The signal feedline 109 may be connected to the
quantum device 145 and a measurement/analysis device 144 via a
circulator 180B. The measurement/analysis device 144 may be
utilized for further processing. In one implementation, the device
144 may represent a 50 ohm termination. The port of the circulator
180B connected to the measurement/analysis device 144 ensures that
no reflected signal is transmitted back to the quantum device
145.
The pump resonator 102 has a fundamental mode, which may be
referred to as the pump mode or pump resonance mode. The pump mode
of the pump resonator 102 has a resonance frequency, which may be
referred to as the pump resonance frequency f.sub.P. The pump mode
of the pump resonator 102 has a wavelength .lamda..sub.P, where
.lamda..sub.P=c'/f.sub.P and c' is the speed of light in the
transmission line or waveguide used in the implementation of the
device 102. The pump signal 130 applied to the pump resonator 102
is a strong coherent resonant tone (i.e., its frequency matches the
resonance frequency of the pump resonator 102). The pump resonator
102 is designed to have a length corresponding to .lamda..sub.p/4,
which is quarter the wavelength of the pump signal. The stubs 120A
and 120B are each designed to have a length corresponding to
.lamda..sub.p/2, which is half the wavelength of the pump
signal.
The signal resonator 104 has a fundamental mode, which may be
referred to as the signal mode or signal resonance mode. The signal
mode of the signal resonator 104 has a resonance frequency, which
may be referred to as the signal resonance frequency f.sub.S. The
quantum microwave signal 140 input to the signal resonator is a
weak resonant tone on the order of a few single photons, whose
frequency f.sub.S matches the resonance frequency of the signal
mode. The signal mode of the signal resonator 104 has a wavelength
.lamda..sub.S, where .lamda..sub.S=c'/f.sub.S and c' is the speed
of light in the transmission line or waveguide used in the
implementation of the device. The signal resonator 104 is designed
to have a length corresponding to .lamda..sub.S/4, which is a
quarter the wavelength of the quantum signal.
The microwave device 100 has a frequency condition between the
(pump) resonance frequency of the pump resonator 102 and the
(signal) resonance frequency of the signal resonator 104. The
frequency condition is that the pump resonance frequency f.sub.P of
the pump resonator 102 is equal to twice the signal resonance
frequency f.sub.S of the signal resonator 104. In other words, the
frequency condition is f.sub.P=2f.sub.S. Accordingly, the applied
signal 130 has a frequency f.sub.P that is twice the frequency
f.sub.S of the quantum signal 140.
The microwave device 100 is configured such that the reflected pump
signal 130 (identified as, e.g., as reflected pump signal 130')
carries information about the number of photons present in the
input quantum signal 140, and thereby can be utilized to count the
photons in the quantum signal 140. Additionally, the reflected
quantum signal 140 (identified as, e.g., reflected quantum signal
140') carries information about the number of photons present in
the input pump signal 130, and thereby can be utilized to count the
photons in the pump signal 130. This information about the number
of photons in the quantum signal 140 is encoded in the phase shift
of the reflected pump signal 130' off port 108 as a result of the
resonance frequency shift of the pump resonator 102 depending on
the number of photons in the signal resonator 104. The phase shift
in the reflected pump signal 130' is measured and analyzed by the
microwave measurement/analysis device 150.
The microwave device 100 (and/or operation via pump signal 130 and
quantum signal 140) is configured such that it can be described by
the effective Hamiltonian (without the drives and feedlines)
H.sub.eff= {tilde over (.omega.)}.sub.PN.sub.P+ {tilde over
(.omega.)}.sub.SN.sub.S+ KN.sub.P.sup.2+ K'N.sub.PN.sub.S, where
{tilde over (.omega.)}.sub.PN.sub.P represents the pump resonance
mode term (modelled as a harmonic oscillator with {tilde over
(.omega.)}.sub.P the dressed resonance frequency of the pump
resonance mode), {tilde over (.omega.)}.sub.SN.sub.S represents the
signal resonance mode term (modelled as a harmonic oscillator with
{tilde over (.omega.)}.sub.S the dressed resonance frequency of the
signal resonance mode), KN.sup.2 represents the self-Kerr
nonlinearity of the device, and K'N.sub.PN.sub.S represents the
cross-Kerr nonlinearity of the device. Further, K is the self-Kerr
constant (i.e., the Kerr frequency shift per photon), and K' is the
cross-Kerr constant (i.e., the cross-Kerr frequency shift per
photon). Additionally, N.sub.P is the photon number operator of the
pump mode (whose eigenvalue is the number of photons in the pump
resonance mode), where N.sub.P=a.sub.P.sup..dagger.a.sub.P, and
N.sub.S is the photon number operator of the signal mode (whose
eigenvalue is the number of photons in the signal resonance mode),
where N.sub.S=a.sub.S.sup..dagger.a.sub.S, and
.times..pi. ##EQU00001## where h is Planck's constant. Also,
a.sub.P and a.sub.S are quantum operators (i.e., annihilation
operators associated with the pump and signal resonance modes). It
is noted that sometimes in this disclosure the symbols N.sub.P,
N.sub.S may be utilized to represent the eigenvalues of the number
operators and not the number operators themselves. It is also noted
that any person who is skilled in the art can easily make this
distinction from the context.
FIG. 2 is a schematic of the equivalent circuit of the microwave
device 100 according to an embodiment as seen by the pump port 111.
In addition to illustrating what the pump port 111 sees, FIG. 2
concurrently illustrates the circuit as seen by the incoming pump
signal 130 at the pump resonance frequency f.sub.P. Accordingly,
discussion regarding the pump port 111 applies to the incoming pump
signal 130.
In the pump equivalent circuit, FIG. 2 shows the pump feedline 108
(including pump port 111) coupled to the transmission line part of
the pump resonator 102 via the coupling capacitor 106A, and the
other end of the transmission line part of the pump resonator
connected to ground via the Josephson junction 110. To explain this
equivalent circuit, it is noted that 1) stub 120A, which serves as
an impedance transformer, is terminated in an open circuit and its
length corresponds to half the wavelength of the pump signal 130,
thus node A sees an open circuit at the pump frequency, and 2) stub
120B, which serves as an impedance transformer, is terminated in a
short circuit and its length corresponds to half the wavelength of
the pump signal 130, thus node B sees a short circuit at the pump
frequency.
One beneficial result of this pump equivalent circuit is that it
shows that the pump resonance mode does not see the signal
resonator 104. In other words, the pump resonator 102 is isolated
from the signal resonator 104.
Another beneficial result is that the rf-current I.sub.P associated
with the pump resonance mode has an anti-node at the location of
the Josephson junction 110.
FIG. 3 is a schematic of the equivalent circuit of the microwave
device 100 as seen by the quantum signal port 113 according to an
embodiment. In addition to illustrating what the signal port 113
sees, FIG. 3 concurrently shows the equivalent circuit as seen by
the incoming quantum signal 140 at the signal resonance frequency
f.sub.S. Accordingly, discussion regarding the signal port 113
applies to the incoming quantum signal 140.
In the equivalent circuit of the microwave device 100 which is seen
by the signal port, FIG. 3 shows the signal feedline 109 (including
signal port 113) coupled to the transmission line part of the
signal resonator 104 via the coupling capacitor 106B, and the other
end of the transmission line part of the signal resonator 104
connected to ground via the Josephson junction 110. Since the
frequency condition for the pump frequency is f.sub.P=2f.sub.S (the
fundamental resonance mode of the pump resonator 102 corresponds to
the pump frequency f.sub.P while the fundamental resonance mode of
the signal resonator 104 corresponds to the signal frequency
f.sub.S), the signal port 113 (quantum signal 140 at the signal
resonance frequency f.sub.S) sees the opposite of the pump port
111.
In this case (i.e., the case of the signal port), stub 120B, which
serves as an impedance transformer, is terminated in a short
circuit and its length corresponds to quarter the wavelength of the
signal, thus node B sees an open circuit at the signal frequency.
Similarly, stub 120A, which serves as an impedance transformer, is
terminated in an open circuit and its length corresponds to quarter
the wavelength of the signal, thus node A sees a short circuit at
the signal frequency.
One beneficial result of this signal equivalent circuit is that it
shows that the signal resonance mode does not see the pump
resonator 102. In other words, the signal resonator 104 is isolated
from the pump resonator 102.
Another beneficial result is that the rf-current I.sub.S associated
with the signal resonance mode has an anti-node at the location of
the Josephson junction 110.
It is noteworthy to clarify here based on FIGS. 2 and 3, that 1)
the pump resonator 102 (ignoring the coupling capacitor and
feedline) consists of the quarter-wavelength transmission line at
the pump frequency shorted to ground via the Josephson junction
110, and 2) the signal resonator 104 (ignoring the coupling
capacitor and feedline) consists of the quarter-wavelength
transmission line at the signal frequency shorted to ground via the
Josephson junction 110.
The microwave device 100 is configured to couple two microwave
resonance modes (i.e., the pump resonance mode and the signal
resonance mode) to a common dispersive nonlinear element, i.e.,
Josephson junction 110.
The microwave device 100 is configured to use one mode, i.e., the
pump mode at the pump resonance frequency f.sub.P, as a photon
number detector of the photons present in the second mode, i.e.,
the quantum signal mode at the signal resonance frequency f.sub.S.
In the microwave device 100, the signal resonance frequency f.sub.S
of the signal mode corresponds to the microwave frequency of the
microwave photons that are to be detected and/or counted.
By driving the pump mode (of the pump resonator 102) using a strong
coherent microwave tone (i.e., pump signal 130) at the pump
resonance frequency f.sub.P, the microwave device 100 is configured
to give rise to a cross-Kerr nonlinear effect in the Josephson
junction 110 which leads to a nonlinear interaction between the
pump and signals modes (and consequently between the pump signal
130 at the pump resonance frequency f.sub.P and the quantum signal
140 at the signal resonance frequency f.sub.S).
As a result of this cross-Kerr effect, the microwave device 100 is
configured such that the pump resonance frequency f.sub.P of the
pump mode becomes dependent on the number of photons in the signal
resonance mode at frequency f.sub.S and vice versa.
The microwave device 100 is configured such that by monitoring the
phase of the reflected pump signal 130' at frequency f.sub.P, the
measurement/analysis device 150 can detect in a quantum
nondemolition measurement the presence or absence of signal photons
in the signal mode (i.e., detect the presence or absence of signal
photons in the quantum signal 140 at frequency f.sub.S).
The microwave device 100 is configured such that the number of
photons in the signal mode is inferred/determined based on the size
of the phase shift acquired by the output pump signal 130' (as
measured in reflection by the measurement/analysis device 150 at
the pump feedline 108). Hence, the microwave device 100 serves as a
nondemolition microwave photon detector and counter. By introducing
a frequency shift in the resonance frequency of the pump mode, the
microwave device 100 neither absorbs nor destroys the signal
photons in the quantum signal 140. Rather, the quantum signal is
reflected off 104' the microwave device 100 at the signal feedline
109 after interacting with the pump signal 130 in the device 100
via the Josephson junction 110.
It is noted that in addition to the pump and signal modes which are
measured in reflection and explained in detail above, the microwave
device 100 has also two common resonance modes which can be
measured in transmission between the pump and signal ports.
However, these common resonance modes do not play a role in the
signal-pump interaction described above and have frequencies that
are far detuned from the pump and signal resonance modes (thus can
be filtered out if necessary). For example, for a device with a
pump resonance frequency around 16 GHz, and a signal resonance
frequency around 8 GHz, the common modes of the device are expected
to resonate at around 3 GHz, and 13 GHz.
Two beneficial advantages of the microwave device 100 which can be
readily inferred from the device description are the following:
1) the strong pump drive (i.e., pump signal 130) which enables the
detection of the signal photons is injected through a different
port than the weak signal (e.g., quantum signal 140) being
detected; and
2) the pump and signal modes are completely isolated from each
other (due to the use of the stubs). They only interact through the
JJ (or JJs) which connects their respective resonators. Hence, by
design there should not be any direct power leakage between the
pump and signal ports.
FIG. 4 is a schematic of the microwave device 100 implemented as a
coplanar waveguide according to an embodiment. In FIG. 4, a pump
feedline 108 is connected to the pump resonator 102 by the coupling
capacitor 106A. The pump feedline 108 and the pump resonator 102
are made of superconductors formed on a low-loss dielectric
substrate. The coupling capacitor 106A is implemented as a gap
capacitor between the conductors of the pump feedline 108 and pump
resonator 102. The pump resonator 102 has a length corresponding to
approximately .lamda..sub.P/4 (for a particular pump resonance
frequency this length can vary depending on the amount of lumped
inductance added by the Josephson junction 110 terminating the
transmission line part of the pump resonator). A ground plane 405
is formed on both sides of the pump resonator 102 and pump feedline
108.
A quantum signal feedline 109 is connected to the signal resonator
104 by the coupling capacitor 106B. The signal feedline 109 and the
signal resonator 104 are also made of superconductors formed on the
low-loss dielectric substrate. Similarly, the coupling capacitor
106B is implemented as a gap capacitor between the conductors of
the signal feedline 109 and signal resonator 104. The signal
resonator 104 has a length corresponding to approximately
.lamda..sub.S/4 (for a particular signal resonance frequency this
length can vary depending on the amount of lumped inductance added
by the Josephson junction 110 terminating the transmission line
part of the signal resonator). A ground plane 405 is formed on both
sides of the signal resonator 104 and signal feedline 109.
At node A, the pump resonator 102 is connected to the Josephson
junction 110 and the stub 120A. The other end of the stub 120A is
left open (i.e., terminated in an open circuit).
At node B, the signal resonator 104 is connected to the Josephson
junction 110 and the stub 120B. The other end of the stub 120B is
connected to the ground plane 405. The stubs 120A and 120B are
superconducting transmission lines implemented in this embodiment
in the form of a coplanar waveguide on the low-loss dielectric
substrate, and the center conductor of the stubs 120A and 120B each
have a length corresponding to .lamda..sub.P/2.
The Josephson junction 110 is a dispersive nonlinear inductor,
which is made of two superconducting electrodes separated by a
barrier (e.g., insulating tunnel barrier). For example, one
superconducting electrode of the Josephson junction 110 connects to
node A, while the other superconducting electrode connects to node
B.
FIG. 5 is a schematic of the microwave device 100 implemented in
the form of a microstrip geometry according to an embodiment. FIG.
5 is similar to FIG. 4 in that the microstrip implementation has
superconductors formed on a low-loss dielectric substrate according
to the microwave device 100. One main difference between the
microstrip and the coplanar waveguide implementations relates to
the location of the ground plane. In the coplanar waveguide
configuration (FIG. 4) the ground plane is located on the same side
of the dielectric substrate as the center conductor, whereas in the
microstrip configuration (FIG. 5) the ground plane is on the
opposite side of the dielectric substrate.
In FIG. 5, a pump feedline 108 is connected to the pump resonator
102 by the coupling capacitor 106A. The pump feedline 108 and the
pump resonator 102 are superconductors formed on a low-loss
dielectric substrate. The coupling capacitor 106A is implemented as
a gap capacitor between the conductors of the pump feedline 108 and
pump resonator 102. The pump resonator 102 has a length
corresponding to .lamda..sub.P/4 (for a particular pump resonance
frequency this length can vary depending on the amount of lumped
inductance added by the Josephson junction 110 terminating the
transmission line part of the pump resonator). However, unlike FIG.
4, no ground plane is formed on both sides of the pump resonator
102 and pump feedline 108, and instead the ground plane is formed
on the other side of the dielectric substrate.
A quantum signal feedline 109 is connected to the signal resonator
104 by the coupling capacitor 106B. The signal feedline 109 and the
signal resonator 104 are also superconductors formed on the
low-loss dielectric substrate. Similarly, the coupling capacitor
106B is implemented as a gap capacitor between the conductors of
the signal feedline 109 and signal resonator 104. The signal
resonator 104 has a length corresponding to .lamda..sub.S/4 (for a
particular signal resonance frequency this length can vary
depending on the amount of lumped inductance added by the Josephson
junction 110 terminating the transmission line part of the signal
resonator). Unlike FIG. 4, no ground plane is formed on both sides
of the signal resonator 104 and signal feedline 109, and instead
the ground plane is formed on the other side of the dielectric
substrate.
At node A, the pump resonator 102 is connected to the Josephson
junction 110 and the stub 120A. The other end of the stub 120A is
left open (i.e., terminated in an open circuit).
At node B, the signal resonator 104 is connected to the Josephson
junction 110 and the stub 120B. The other end of the stub 120B is
connected to the ground plane 405. The stubs 120A and 120B are
superconducting transmission lines implemented in this embodiment
in the form of a microstrip on the low-loss dielectric substrate,
and the center conductor of the stubs 120A and 120B each have a
length corresponding to .lamda..sub.P/2.
In accordance with the teachings presented herein, one of ordinary
skill in the art recognizes other possible implementations or
variations to embodiments. In one implementation, the pump and
signal resonators 102 and 104 may be equivalently implemented using
lumped inductors (e.g., narrow superconducting wires or array of
large Josephson junctions) and lumped capacitors (e.g., planar
capacitors or interdigitated capacitors). One particular condition
in the various implementations is to maintain maximum RF currents
of the pump and signal modes at the Josephson junction 110
location.
In another implementation, the half-wave stubs 120A and 120B of the
microwave device 100 can also implemented using their equivalent
lumped-element circuit in the vicinity of the pump resonance
frequency.
In one implementation, the single Josephson junction 110 may be
replaced by an array of large Josephson junctions.
In yet another implementation, the single Josephson junction 110
may be replaced by a direct current superconducting quantum
interference device (DC-SQUID) (or array of DC-SQUIDs) which
enables in-situ tuning of the linear inductance of the mixing
element (i.e., the inductance of the Josephson junctions in the
DC-SQUID) by varying the magnetic flux threading the DC-SQUID loop
(or the loops of the array of DC-SQUIDs).
According to an implementation, the microwave device 100 can be
made frequency tunable by incorporating DC-SQUIDs in the device
resonators, stubs, and the nonlinear mixing element (i.e., the
Josephson junction 110 or array of Josephson junctions).
More detail of the theory for the photon counting and detection in
the microwave device 100 is discussed. For ease of understanding,
sub-headings are provided below. It is understood that the
sub-heading are for explanation purposes and not limitation.
I. The Energy of the Josephson Junction
A supercurrent flowing in a Josephson junction satisfies the
current-phase relation given by I.sub.J=I.sub.0 sin .delta., where
I.sub.0 is the critical current of the Josephson junction, .delta.
is the gauge-invariant phase difference. The energy of the
Josephson junction can be written as E.sub.j=E.sub.j[1-cos
.delta.], where E.sub.j=I.sub.0.phi..sub.0 is the Josephson energy
and .phi..sub.0= /2e is the reduced flux-quantum (e is the electron
charge). By using the trigonometric identity cos x= {square root
over (1-x.sup.2)} we can rewrite the energy of the Josephson
junction as E.sub.j=
.function. ##EQU00002##
Expanding the expression for the energy of the Josephson junction
up to fourth order in current we get
.times..times. ##EQU00003## By substituting the junction
inductance
##EQU00004## we obtain
.times..times..times. ##EQU00005##
where the first term (.varies.I.sub.J.sup.2) modifies the bare
resonance frequencies of the pump and signal resonators while the
second term (.varies.I.sub.J.sup.4) represents the nonlinear mixing
term.
II. Quantization
Based on the equivalent circuits of the microwave device as seen by
the pump and signal ports shown in FIGS. 2, 3, the Radio frequency
(RF) current flowing in the Josephson junction is
I.sub.J=I.sub.P-I.sub.S, where I.sub.P and I.sub.S are the
rf-currents of the pump and signal microwave resonance modes
flowing in the Josephson junction.
Expressing the currents I.sub.P, I.sub.S in terms of the quantum
operators a.sub.P, a.sub.S which represent the annihilation
operators associated with the pump and signal resonance modes gives
I.sub.P=iI.sub.P(a.sub.P.sup..dagger.-a.sub.P) (Eq. 2)
I.sub.S=iI.sub.S(a.sub.S.sup..dagger.-a.sub.S) (Eq. 3)
where I.sub.P, I.sub.S are the zero-point fluctuations (ZPF)
current amplitudes given by
.omega..times.
.times..times..times..times..times..times..omega..times.
.times..times. ##EQU00006## where .omega..sub.P and .omega..sub.S
are the angular resonance frequencies of the pump and signal
resonators, and Z.sub.P and Z.sub.S are the characteristic
impedances of the corresponding resonators.
Using the following expressions for the angular resonance
frequencies
.omega..times..omega..times. ##EQU00007## and resonator
impedances
##EQU00008## the ZPF current amplitudes can be rewritten as
.times..omega..times. .times..omega..times. ##EQU00009##
where L.sub.P, L.sub.S and C.sub.P, C.sub.S represent the
inductances and capacitances of the equivalent LC circuit of the
pump and signal resonators at resonance.
III. Effective Hamiltonian of the System
Without taking into account the feedlines, drives, and loss to the
environment the effective Hamiltonian of the system is given by the
sum H.sub.eff=H.sub.res+E.sub.j, (Eq. 6)
where H.sub.res= .omega..sub.PN.sub.P+ .omega..sub.SN.sub.S, and
N.sub.P=a.sub.P.sup..dagger.a.sub.P,
N.sub.S=a.sub.S.sup..dagger.a.sub.S are the photon number operators
for the pump and signal modes.
Substituting Eqs. 2 and 3 into the expression for E.sub.j (i.e.,
Eq. 1) while using Eqs. 4 and 5, the photon number operators
N.sub.P, N.sub.S, the imposed frequency condition
.omega..sub.P=2.omega..sub.S, and the rotating wave approximation,
we can write the effective Hamiltonian of the system (Eq. 6) in the
form H.sub.eff= {tilde over (.omega.)}.sub.PN.sub.P+ {tilde over
(.omega.)}.sub.SN.sub.S+ KN.sub.P.sup.2+ K'N.sub.PN.sub.S, (Eq.
7)
where {tilde over (.omega.)}.sub.P, {tilde over (.omega.)}.sub.S in
the first and second term are the dressed angular resonance
frequencies of the pump and signal modes which include the
inductive loading of the resonators due to the Josephson junction
(represented by the first term in Eq. 1), and K, K' in the third
and fourth term which represent the self-Kerr and cross-Kerr
nonlinearity correspond to the self-Kerr and cross-Kerr constants
respectively.
In the derivation of Eq. 7, we have also used the fact the pump
mode is driven strongly compared to the signal mode, and that the
bosonic operators of the two modes a.sub.P, a.sub.S commute with
each other and those of the same mode satisfy the usual commutation
relations of the form [a.sub.P, a.sub.P.sup..dagger.]=1, [a.sub.S,
a.sub.S.sup..dagger.]=1.
The self-Kerr constant in Eq. 7 is given by
.times..times. ##EQU00010## which we can rewrite in terms of the
participation ratio
##EQU00011## of the linear inductance of the JJ to the total
inductance of the pump resonator and the plasma frequency of
the
.times..times..omega..times. ##EQU00012##
.times..omega..times..times..omega..times. ##EQU00013##
Similarly, the cross-Kerr constant in Eq. 7 is given by
'.times..times. ##EQU00014## which we can rewrite in terms of
p.sub.P, .omega..sub.J, and the participation ratio
##EQU00015## of the linear inductance of the JJ to the total
inductance of the signal resonator
'.times..times..omega..times..omega..times..omega..times.
##EQU00016##
IV. Resonance Frequency Shift Per Photon
To better understand the basic idea of the device, we rearrange the
terms in Eq. 7 such that the effective Hamiltonian of the system
reads H.sub.eff= ({tilde over
(.omega.)}.sub.P+KN.sub.P+K'N.sub.S)N.sub.P+ {tilde over
(.omega.)}.sub.SN.sub.S. (Eq. 10)
This form shows that by operating the device in the nonlinear
regime where the Kerr effect is appreciable, the self-Kerr and
cross-Kerr nonlinearity cause the dressed angular resonance
frequency of the pump mode to shift depending on the number of
photons present in the pump and signal resonance modes.
Furthermore, since the pump mode is externally driven at a certain
working point, signal photons that enter the signal resonator would
shift the pump resonance frequency by K'N.sub.S, which is
proportional to their number, thus the cross-Kerr constant K'
corresponds to frequency shift per photon.
It is noted that in order to detect (i.e., resolve the presence of)
a single microwave photon using this device the frequency shift per
photon due to the cross-Kerr nonlinearity (i.e., K') should be
equal or larger than the linewidth (i.e., bandwidth) of the pump
resonance mode at the working point.
V. Design Example Using Typical Numerical Values
In a design example of the proposed microwave device 100, feasible
numerical values of the various parameters are utilized. The
dressed resonance frequency for the pump mode is
.omega..times..pi..times..times. ##EQU00017## The dressed resonance
frequency for the signal mode is
.omega..times..pi..times..times. ##EQU00018## The impedance of the
resonators Z.sub.P=Z.sub.S=50.OMEGA. (please note that lower
characteristic impedances are also feasible and are expected to be
more favorable with respect to the device performance). Using the
relation
.omega. ##EQU00019## we get an estimate for L.sub.P=0.5 nanoHenry
(nH), L.sub.S=1 nH. Assuming I.sub.0=1 microampere (.mu.A), then
L.sub.J=0.3 nH and
.omega..times..pi..times..times. ##EQU00020## Using the values for
L.sub.P,S and L.sub.J we get an estimate for the participation
ratios for the pump and signal resonators p.sub.P.apprxeq.0.38 and
P.sub.S.apprxeq.0.23. Substituting these values in Eqs. 8 and 9
yields
.times..pi. .times..times..times..times..times..times.'.times..pi.
.times..times..times. ##EQU00021## By designing the pump resonance
mode to have a linewidth smaller than these frequency shifts per
photon (which is completely achievable with state-of-the-art
superconducting microwave circuits), the microwave device 100 is
configured to detect single quantum signal photons as measured by
the measurement/analysis device 150.
In order for the device to work properly in one implementation, it
needs to satisfy two additional requirements. For the first
requirement, the internal quality factor of both resonators should
be as high as possible at the single photon level >10.sup.5 and
at least 2 orders of magnitude larger than the external quality
factor of the resonators set by the coupling capacitors between the
resonators and the feedlines and their characteristic impedances.
This requirement is so that the signal photons being detected and
the pump photons detecting them do not get lost to internal loss
mechanisms in the resonators at a higher rate than the rate at
which they enter and leave both resonators. One obvious consequence
of this requirement is that the total quality factor of both
resonators is mainly set by the external quality factor.
For the second requirement, the bandwidth of the pump resonator at
the bias point should be equal or larger than the bandwidth of the
signal resonator. In other words, the response time of the pump
resonator should be equal or shorter than the response time of the
signal resonator. This requirement is in order to allow a
sufficient time for the pump photons to detect the signal photons
before they leave the device through the signal feedline. It is
noted that both requirements are achieved in superconducting
microwave circuits discussed herein.
In one implementation, a technique to (experimentally) calibrate
the value of the cross-Kerr constant K' for a certain pump drive is
by varying the input power of a coherent tone applied at the signal
frequency to the signal resonator while measuring--for each input
power--the complex reflection parameter of the pump resonator as a
function of frequency using a very weak probe (less than one photon
on average) superimposed on the pump drive. By extracting the slope
of the measured pump resonance frequency versus signal power and
using beforehand knowledge of the signal resonance frequency and
the signal resonator bandwidth, one can calculate the constant
K'.
In one implementation, a technique to (experimentally) detect
single signal photons using this device is by monitoring the phase
of the reflected pump drive applied at the pump resonance frequency
with no input signal (i.e., N.sub.S=0). When signal photons on the
order of 1-3 photons enter the signal resonator and interact with
the pump mode through the JJ (i.e., the nonlinear dispersive
element) the resonance frequency of the pump mode shifts downwards
by a multiple number of K'/2.pi. that is proportional to the number
of signal photons in the signal resonator. As a consequence of this
resonance frequency shift of the pump mode, the phase of the
reflected pump drive is correspondingly shifted as well. By
measuring this phase shift one can infer the number of signal
photons (on the order of 1-3) that entered the device.
In order to count in real-time a larger number of incoming signal
photons, e.g., between 3 to 10, using the device, one may employ a
more elaborate measurement technique. For example, continuous
monitoring may be performed of the reflected phase of multiple
relatively weak tones (in order not to alter the device operation)
applied to the pump resonator at frequencies that are located
'.times..pi..times.'.times..pi..times..times..times.'.times..pi..times.
##EQU00022## below the pump resonance frequency with no input
signal (i.e., N.sub.S=0). According to this method, if a phase
shift is detected in the reflected weak tone that is applied at
frequency
.times.'.times..pi. ##EQU00023## below the pump resonance frequency
with no input signal (i.e., N.sub.S=0), this indicates with high
probability that the incoming signal contained N.sub.S photons.
Measuring a larger number of microwave photons beyond a few photons
might not be as useful for certain quantum applications, and thus
the device may not be tuned accordingly. It is also noted that the
effective Hamiltonian of the system was specifically derived in the
limit of very weak signal compared to the pump drive. Thus, by
further increasing the strength of the signal beyond a few photons,
other unwanted nonlinear terms which were neglected in the
derivation of the Hamiltonian (Eq. 10) are expected to come into
play. The exact number of input signal photons which the device can
detect or count without a significant degradation of performance
can of course vary from one device to another and from one
implementation to another depending on several design parameters,
such as the critical current of JJ or JJs, the participation
ratios, the bandwidths of the resonators, the characteristic
impedances of the resonators, and the particular implementation of
the resonators.
Now turning to FIG. 6, a flow chart of a method 600 is provided for
nondemolition counting and/or detection of microwave photons using
the microwave device 100 according to an embodiment.
At block 605, the microwave device 100 is configured to couple a
pump resonance mode (fundamental resonance mode) of the pump
resonator 102 and a signal resonance mode (e.g., fundamental
resonance mode) of the quantum signal resonator 104 to a dispersive
nonlinear element (e.g., Josephson junction 110), responsive to the
pump signal 130 at a pump resonance frequency f.sub.P and the
quantum signal 140 at a signal resonance frequency f.sub.S. The
pump resonance mode of the pump resonator 102 has the pump
resonance frequency f.sub.P and the signal resonance mode of the
quantum signal resonator has the signal resonance frequency.
At block 610, the microwave device 100 is configured to create a
nonlinear interaction\mixing (i.e., via the Josephson junction 110)
between the pump signal 130 and the quantum signal 140, by strongly
driving the pump resonance mode (i.e., pump mode) with the coherent
pump signal 130 at the pump resonance frequency f.sub.P.
At block 615, the microwave device 100 is configured to enable
detection of the presence or absence of photons in the quantum
signal 140 according to the resonance frequency of the pump mode
which affects the phase of the output pump signal 130' (i.e.,
reflected from the microwave device 100).
The microwave device 100 is configured to excite a cross-Kerr
nonlinear effect in the dispersive nonlinear element, thereby
causing the nonlinear interaction between the pump signal 130 and
the quantum signal 140. The microwave device 100 is configured such
that the pump resonance frequency of the pump mode is dependent on
the number of photons in the quantum signal 140 as a result of the
cross-Kerr nonlinear effect taking place in the device (this can be
shown by taking into account the input-output relations of the
device).
The number of photons in the quantum signal 140 is determined by a
size of a frequency shift in the pump resonance frequency. The
frequency shift is a multiple of a cross-Kerr coefficient. A
baseline frequency shift is established, such that the frequency
shift is denoted as being greater than the baseline frequency shift
previously established. The frequency shift denotes the number of
the photons in the quantum signal while the baseline frequency
shift is established prior to receiving the quantum signal. Each
multiple of the baseline frequency shift in the pump signal denotes
a single photon count of the quantum signal, such that 0-N photons
corresponds to 0-M multiples of the baseline frequency shift, where
N is a last number of the photons and M is a last multiple of the
baseline frequency shift.
FIG. 7 is a flow chart of a method 700 for the microwave device 100
according to an embodiment. Reference can be made to FIGS. 1-5.
At block 705, the microwave device 100 is configured to receive a
strong coherent pump signal 130 at the pump resonance frequency
f.sub.P, where the pump resonance frequency corresponds to a pump
resonance (fundamental) mode of a pump resonator 102.
At block 710, the microwave device 100 is configured to receive a
quantum signal 140 at the signal resonance frequency f.sub.S, where
the signal resonance frequency corresponds to a signal resonance
(fundamental) mode of a signal resonator 104.
At block 715, the microwave device 100 is configured to output the
pump signal 130' with a phase shift, in response to pump resonance
frequency shift of the pump mode which depends on a number of
photons in the quantum signal 140.
It will be noted that various microelectronic device fabrication
methods may be utilized to fabricate the components/elements
discussed herein as understood by one skilled in the art. In
superconducting and semiconductor device fabrication, the various
processing steps fall into four general categories: deposition,
removal, patterning, and modification of electrical properties.
Deposition is any process that grows, coats, or otherwise transfers
a material onto the wafer. Available technologies include physical
vapor deposition (PVD), chemical vapor deposition (CVD),
electrochemical deposition (ECD), molecular beam epitaxy (MBE) and
more recently, atomic layer deposition (ALD) among others.
Removal is any process that removes material from the wafer:
examples include etch processes (either wet or dry), and
chemical-mechanical planarization (CMP), etc.
Patterning is the shaping or altering of deposited materials, and
is generally referred to as lithography. For example, in
conventional lithography, the wafer is coated with a chemical
called a photoresist; then, a machine called a stepper focuses,
aligns, and moves a mask, exposing select portions of the wafer
below to short wavelength light; the exposed regions are washed
away by a developer solution. After etching or other processing,
the remaining photoresist is removed. Patterning also includes
electron-beam lithography.
Modification of electrical properties may include doping, such as
doping transistor sources and drains, generally by diffusion and/or
by ion implantation. These doping processes are followed by furnace
annealing or by rapid thermal annealing (RTA). Annealing serves to
activate the implanted dopants.
The flowchart and block diagrams in the Figures illustrate the
architecture, functionality, and operation of possible
implementations of systems, methods, and computer program products
according to various embodiments of the present invention. In this
regard, each block in the flowchart or block diagrams may represent
a module, segment, or portion of instructions, which comprises one
or more executable instructions for implementing the specified
logical function(s). In some alternative implementations, the
functions noted in the block may occur out of the order noted in
the figures. For example, two blocks shown in succession may, in
fact, be executed substantially concurrently, or the blocks may
sometimes be executed in the reverse order, depending upon the
functionality involved. It will also be noted that each block of
the block diagrams and/or flowchart illustration, and combinations
of blocks in the block diagrams and/or flowchart illustration, can
be implemented by special purpose hardware-based systems that
perform the specified functions or acts or carry out combinations
of special purpose hardware and computer instructions.
The descriptions of the various embodiments of the present
invention have been presented for purposes of illustration, but are
not intended to be exhaustive or limited to the embodiments
disclosed. Many modifications and variations will be apparent to
those of ordinary skill in the art without departing from the scope
and spirit of the described embodiments. The terminology used
herein was chosen to best explain the principles of the
embodiments, the practical application or technical improvement
over technologies found in the marketplace, or to enable others of
ordinary skill in the art to understand the embodiments disclosed
herein.
* * * * *